GRAIN BOUNDARY GEOMETRY AND

INTERGRANULAR CRACK PROPAGATION IN N&Al AND Ir

Hui Lin and David P. Pope

Department of Materials Science and Engineering, University of Pennsylvania 3231 Walnut Street, Philadelphia, PA 19104, U.S.A.

Abstract

The distribution of grain boundary types along intergranular cracks in B-free Ni3Al and pure Ir

was measured, by C value, and compared to the distribution in the bulk, using statistically

significant sample sizes. It was found that low angle (Cl) and symmetrical X3 boundaries

(twins) are particularly strong. All other high boundaries have similarly low strength, independent

of their C values, in particular, low C, high angle boundaries, as a group, are not strong. These

results qualitatively agree with predictions based on the structural unit model and imply that 1) Ni3Al and Ir have similar boundary structure and 2) the fracture strength of an intergranularly

brittle polycrystalline aggregate can be increased only by increasing the fraction of low angle and

symmetrical C3 boundaries.

The authors wish to thank Dr. John Liu of ALCOA Technical Center and Dr. John Hack of Yale

University for providing access to their EBSP facilities. This work was supported by the NSF

MRL program under grant number DMR-88-19885 through the Laboratory for Research on the

Structure of Matter at the University of Pennsylvania.

Superalloys 1992 Edited by SD. Antolovich, R.W. Stusrud, R.A. MacKay,

D.L. Anton, T. Khan, R.D. Kissinger, D.L. Klarstrom The Minerals, Metals & Materials Society, 1992

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Introduction

This paper deals with the relationship between the structure and intrinsic cracking resistance of

grain boundaries in fee materials and fee-based ordered intermetallic compounds. The

experimental program centers on one simple case, intergranular fracture at low temperatures

caused by the intrinsic weakness of grain boundaries, thereby avoiding the complexities

associated with diffusion and/or impurity induced intergranular cracking and making it possible to reveal the purely structural relations. If the variation in fracture strength among grain boundaries

of different character is sufficiently large that a class of strong boundaries can be identified then

materials prone to intergranular cracking may be toughened by increasing the abundance of those

“strong boundaries”, a process called “grain boundary engineering” [ 1, 21. Based on the

information currently available in the literature [3-8], low angle (Cl) and Z3 boundaries in both

fee and bee materials and possibly Cl lb { 113}/( 113) and C17b (223}/{ 223) twin boundaries in bee materials are the only experimentally observed strong boundaries. Other boundaries, including a number of other low C boundaries, show lower and approximately equal strengths. However the statistical significance of much of these data is open to question.

We have identified types of strong boundaries in a statistically significant manner by performing

specially designed bending tests on B-free Ni3Al (Ll;! intermetallic) and pure Ir (fee element)

polycrystalline specimens. B-free Ni3Al and Ir were chosen as the model materials in our study

because they fail in a brittle intergranular manner at room temperature, even when the boundaries

are impurity-free [9-131. We have used specimens that are one grain thick, thereby avoiding the complications in the stress state due to subsurface grains. The stress state in such a specimen under bending can be approximated by that in a rectangular beam and the only non-zero stress

component is an axial tensile stress which is maximal at the surface. Our approach is to first

fracture the sample, then replace the broken pieces in their original, correct relative orientations,

and then measure the grain orientations across the broken boundaries. The distributions of

boundary types along the crack is then compared with the distribution obtained from the bulk to

see if there are differences. The boundaries missing from the crack faces are then the strong grain

boundaries. We have chosen to use C values from the CSL model , for reviews see [14-171, to classify boundaries, as have most previous investigators [8, 18-211. We are also able to determine the boundary plane for certain boundaries and have done so for one set of strong boundaries.

The objectives of this study are: (1) to fully establish the phenomenological relationship between

grain boundary structure and intergranular crack propagation, (2) to identify which are the “strong

boundaries”, and (3) to relate the experimental results to the theory of boundary structure. This

study is made possible by three factors: the use of one-grain-thick specimens, the ability to

replace the cracked faces in their original positions, and the use of a semi-automated electron

backscattering pattern (EBSP) technique to quickly orient a large number of grains.

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ExnerimentaI

Melt-spun NisAl ribbons (75.0 at.% Ni, 24.8 at.% Al and 0.2 at.% Ta, about

15mmx3mmx20~m) were used as specimens. These ribbons were first annealed at 1200°C for one hour in a 10-6 torr vacuum to allow individual grains to grow through the thickness of the

ribbons. Both surfaces of the annealed ribbons were then mechanically polished to remove the

alumina/spine1 scale. A second anneal was then necessary to obtain sharp EBSP images. Two

different treatments were used: one, which reveals grain boundaries through thermal etching, is a

one-hour anneal at 1200°C in a 10-h torr vacuum with a graphite oxygen getter, and the other,

which results in no etching, is the same treatment at a temperature of 800°C. The Ir specimens (1Smmx1Ommx40~m) were made from hot-rolled sheets (99.99%) which were subsequently treated similarly to the N&AI ribbons except that the first anneal was at 1700°C for 24 hours and the second anneal was at 1200°C for one hour resulting in a slight thermal etching.

A piece of Ni3Al or Iridium ribbon thus prepared is then bonded with M-Bond 200 adhesive to a

piece of clean 100 l.tm-thick aluminum foil using the same procedure as for mounting strain gages

[22]. The composite is bent in air around an edge having a 3 mm radius of curvature to produce

cracks in the ribbon. The whole piece is then flattened between two steel blocks and mounted on

an SEM sample mount using carbon paint as an adhesive. (There are more than 3000 grains within the total bent region and about 50 grains in a given cross section, all under more or less the

same tensile stress during bending. This means that there is a large number of grain boundaries available for crack initiation during any given bending test, and therefore the crack path is selected

by the fracture process itself rather than by a localized stress concentration.)

The crystallographic orientations of individual grains, from which r&orientations of grain-pairs

are calculated and C values are assigned [23], were measured using the electron backscattering

pattern (EBSP) method [24]. For all cubic systems the CSL relations are identical [25], thus the CSL relations for an L12 lattice are calculated in the same way as for an fee lattice. We use the

Brandon criterion [26] as the upper limit for near-coincidence boundaries, assign the lowest c

value to a boundary if it qualifies for more than one near-x boundary, and arbitrarily set the upper

limit of low C boundaries as X=49.

Results

Due to the limitation of space, we will only show the results from thermally etched NisA1 specimens with small cracks, Fig. la, and slightly etched Ir specimens with long cracks, Fig. lb.

However, the distribution of types of cracked boundaries is unaffected by thermal-etching of the grain boundaries and by changing the length of cracks from a few grain boundaries to a few

hundred grain boundaries long [27]. Fracture surfaces of NisAl and Iridium ribbon are shown in

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Figs. 2a and 2b, respectively. Specimens used in this study are slightly textured-Ni3Al has a

~1117 and Ir has a 4007 texture.

Fig. 1 Scanning electron micrographs (SEMs) showing the surface of (a), on the left, a thermally etched Ni3Al specimen with small cracks (bright region) and (b), on the right, a slightly etched Ir specimens with long cracks (dark region). Each individual marker is 10 l.trn long.

Fig. 2 SEMs of the intergranular surface of (a), on the left, an Ni3Al and (b), on the right, an Ir specimen. Note that both specimens are one grain thick. Each marker is 10 pm long.

Thermally etched NiqAl svecimen with small cracks -

Table I lists in columns 2 and 3 the distribution of low angle, ~3, low c and high z boundaries at

random positions, by number and by percentage, respectively; in column 4, the 90% confidence intervals for 155 cracked boundaries, with the proportions in column 3 taken as the true proportions; in columns 5 and 6, the distribution of cracked low angle, x.3, low C and high I; boundaries in specimen 1, by number and by percentage, respectively; and in column 7, whether

the percentages of cracked boundaries fall into their respective 90% confidence intervals*. The 90% confidence intervals are used as a check to see if the collected data scatter within some

reasonable range of certain target values [28]. The data for 3~x125, a subset of the data for

3~x149, are included to check the possible effect of the arbitrary upper limit of low Z boundaries. The same data are also plotted in Fig. 3a.

*The 90% confidence interval is the interval about the true mean of a distribution such that the probability is 0.9 that the mean of a sample of size N from that distribution will lie in that interval.

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Table I The distribution of cracked boundaries compared with that in the general population in a thermally etched N&Al specimen with small cracks.

Grain General Population Cracked Boundary (A Total of 280 GB’s) (A Total of 155 GB’s) Type by I; No. Percent 90% interval for No. Percent Within

value 155 GB’s Interval?

low angle 21 7.5% 4.5-11.0% 3 1.9% no

c3 79 28.2% 22.6-33.5% 3 1.9% no

(3 ~~525) (12) (4.3%) (1.9-7.1%) (8) (5.8%) yes 3.~~549 16 5.7% 3.2-8.4% 11 7.1% Yes

zd > 49 164 58.6% 52.3-65.2% 138 89.0% no

Total 280 100% 155 100%

The total percentages of low c boundaries (3 < c 5 25) in the general population is slightly

different from that of an ideal untextured material, which is 7.47% [29]. For the two groups of

low z boundaries, 3 < z I 25 and 3 < c 149, the total percentages along cracks are close to that in

the general population and lie within the 90% confidence limits. The similarity between the two sets of data indicates that the upper limit of low z boundaries is indeed arbitrary and insignificant.

The percentages of low angle and ~3 boundaries is much lower along cracks than those in the

general population, indicating that these types of grain boundaries are resistant to intergranular cracking. The difference of about 20 percent in the proportion of high c boundaries can be

attributed to the deficit of low angle and ~3 boundaries along the crack.

As a check to see if the boundary distribution in the general population is representative of the

distribution in the area near the cracks, table II compares the distribution of boundary types near

the cracks (within 4-5 grains from the cracks) with that in the general population. The same data

are also plotted in Fig. 3b. Note that the proportion of C3 boundaries at the two positions appears

to be different. This suggests that the crack tends to select regions of the sample where there is a slightly lower fraction of ~3 boundaries. The distribution of the remaining types of boundaries

near cracks agrees well with that in the general population.

Table II The distribution of near-crack boundaries compared with that in the general population in a thermally etched NisAl specimen with small cracks.

Grain General Population Near Crack Boundary (A Total of 280 GB’s) (A Total of 259 GB’s) Type by z No. Percent 90% interval for No. Percent Within

value 259 G.B.s Interval?

low angle 21 7.5% 5.0- 10.0% 24 9.3% Yes c3 79 28.2% 23.9-32.4% 56 21.6% no

(3czS25) (12) (4.3%) (2.3-6.2%) (9) (5.3%) yes 3~x549 16 5.7% 3.5~8.1% 17 6.6% Yes

z > 49 164 58.6% 53.7-63.3% 162 62.5% Yes Total 280 100% 259 100%

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1;1 GmeralG9 Total 280

q CfachdGB Total 155

23 3<2525 3<2s49 G49

I: Value c3 3<2525 3<2<49 L-49

I: Value

Fig. 3 The distribution of grain boundary types by I; values for (a), on the left, cracked and (b), on the right, near-crack grain boundaries compared to that in the general population in an NisAl specimen. The data are taken from table I and II, respectively.

Since 23 grain boundaries are found to resist intergranular cracking we set out to measure the

grain boundary planes of these boundaries using the stereographic projection method [23]. We

have arbitrarily defined a X3 boundary as being a near-symmetrical twin if the boundary plane

deviates by no more than 5” from the { 111) or ( 112) plane. For simplicity, we will call a near-

symmetrical C3 boundary as a symmetrical ~3 boundary, analogous to a near-coincidence boundary. A total of 20 ~3 grain boundaries were randomly chosen out of the previously-indexed

C3 boundaries in the specimen and the boundary planes were determined. The majority of the ~3 grain boundaries are symmetrical twins with either ( 11 1 )/{ 111) or ( 112]/{ 112) planes, see

Table III. The three ~3 boundaries in the specimen which broke during bending were all found to

be non-symmetrical ~3 boundaries.

Table IJJ The distribution of types of ~3 boundaries in a NisAl specimen.

Types of ~3 Boundary Number Percent

non-symmetrical 2 10% symmetrical (112]/( 112) 5 25% symmetrical (111)/(111) 13 65%

Total 20 100%

Slirrhtly etched Ir snecimen with long cracks

The distribution of cracked boundaries along long cracks is listed in table III and compared with that of the general population. The same data are also plotted in Fig. 4. Note the similarity in the results for NisAl and Ir (compare Figs. 3a and 4).

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Table IV The distribution of cracked boundaries compared with that in the general population in a slightly etched Iridium specimen with long cracks.

Grain General Population Cracked Boundary (A Total of 206 GB’s) (A Total of 83 GB’s) Type by z No. Percent 90% interval for No. Percent Within

value 83 GB’s Interval?

low angle 17 8.2% 3.6- 12.0% 0 0.0% no

c3 48 23.3% 20.5-36.1% 2 2.4% no

(3 c z I25) (11) ‘(5.3%) (l.l-7.2%) (6) (7.2%) yes 3<CI49 15 7.3% 2.4-9.6% 7 8.4% yes

x > 49 126 61.2% 50.6-67.5% 74 89.2% no Total 206 100% 83 100%

iii GeneralGB Total 206

q Cradad GB Total 55

x3 3<2<25 3<2<49 x,49

X Value

Fig. 4 The distributions of grain boundary types by C values for cracked grain boundaries compared to that in the general population in an Ir specimen with long cracks. The data are taken from table IV.

- - - -

Fig. 5 A relaxed X5 (310) symmetrical tilt boundary in Ni3Al[39]. The darker circles are Ni atoms and lighter ones are Al atoms. Note the cavities in the boundary.

Discussion

Implication of the results. nucleation vs. nronagation

The distribution of boundary types along a crack depends on both the crack propagation path and

the crack initiation sites if a given crack contains more than one initiation site. However the small,

unconnected cracks (about 10 grain boundaries long) probably have only one initiation site for

each crack and therefore the initiation sites constitute about 10% of the total for the short cracks

and a smaller fraction for the longer cracks. Furthermore, since the fracture surfaces were not

exposed, these nucleation sites cannot be easily identified. This means that correlations between boundary geometry and crack path made in this study relate mainly to crack propagation and contain little information about nucleation. Consequently, we conclude that C value has little

effect on crack DronaPation in Ni3Al and Ir since low C and high C boundaries fail with equal

probability, except for Cl and symmetrical X3 (twins). These two kinds of boundaries resist

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crack propagation and therefore are strong. Other boundaries have similarly low strengths, in

particular,.low C boundaries, as a group, are not strong.

Comnarison with theoretical models

The fact that low angle and symmetrical C3 boundaries are strong and other boundaries have

similarly low strengths, independent of c, is in accord with the implications of the structural unit

model [30-341. According to this model, for pure tilt boundaries, certain favored boundaries with

only one type of units are the fundamental structural units of longer-period, or non-favored, tilt

boundaries. A non-favored boundary in the misorientation range between those of the two

successive favored boundaries is composed of well-defined mixtures of two different units of the

two favored boundaries. The closer the misorientation is to one favored boundary, the more units of that favored boundary the non-favored boundary contains, and the boundary structure changes

continuously throughout the misorientation range. Favored boundaries are generally low C

boundaries [32], but not all low C boundaries are favored boundaries. Since the structure of a

boundary having a misorientation angle between those of two favored boundaries is just a

combination of the structural units of those two boundaries, the properties of the boundary are expected to vary continuously between those of the two favored boundaries. That is, a high C boundary can have properties, such as cohesion and the ability to produce local shear, similar to that of a low C boundary since favored boundaries are, generally, low C boundaries. In

particular, when one of the favored boundaries is the ideal lattice, or has a structure similar to that

of the ideal lattice, then boundaries containing units of this particular favored boundary should

have properties similar to that of the ideal lattice.

Crack propagation is believed to be the results of low cohesion and difficulty in producing local

shear [35], and we think this is equally true for Ni3Al (ordered fee) and Ir (fee). However, we

will focus on Ni3Al in the following discussion (much is understood about the structure of grain

boundaries in NisAl but little about that in Ir) then draw some parallels between Ir and Ni3Al.

Ni3Al is ductile in single crystalline form-the ideal lattice has high cohesion and can easily plastically deform, both locally and globally. Therefore any boundary containing large portions of

the ideal lattice should also possess these qualities. Low angle boundaries are essentially ideal

lattice containing periodically-spaced dislocation cores [36]. The interfacial region in a C3 [111)/(111} b oundq has a structure identical to that of the ideal lattice and a 23 ( 112}/{ 112)

boundary has an interface slightly distorted from that of the ideal lattice, based on simulations of

grain boundary structure using empirically-constructed interatomic potentials [37]. Thus low

angle and symmetrical C3 boundaries should be able to resist crack propagation and therefore be strong, and our results confirm this prediction. Most other boundaries cannot resist crack

propagation because they are structurally different from the ideal lattice and contain defects.

Takasugi and Izumi first postulated that strongly ordered intermetallics have cavities in certain low

Z boundaries based on geometrical considerations and the assumption that strict chemical

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bonding is maintained up to the boundaries [38]. Later, Vitek et al found large cylindrical cavities

of atomic size in strongly ordered intermetallics similar to NisAl, see Fig. 5, based on atomistic

studies of a number of favored symmetrical tilt boundaries [39]. There are varying degrees of

distortion in different favored boundaries and the same distortions are inherited in the non-favored

boundaries. As a result, the boundaries which contain cavities is expected to have much lower

local cohesive strengths than that of those without cavities (due, perhaps, to the heterogeneity of

the electron density in the boundaries [40]) and difficulty of producing local shear (due to the irregular arrangement of atoms near the boundaries). Therefore high angle boundaries,

independent of their C values, are expected to be less resistant to crack propagation and our

results confirm this prediction.

We suspect that the above reasoning would be applicable to Ir even though little is known about

the structure of grain boundaries in that material. The similarity in intergranular cracking-

resistance between NisAl and Ir may be a result of a similarity in the grain boundary structure.

High angle boundaries in Ir may also have cavities because Ir has some fundamental properties

similar to those of NisAl. For example, the Cauchy pressure, C12-c44, for Ir is negative while it

is positive for most ductile fee materials [39]. Similarly, the Cauchy pressure for NisAl and other early transition metal trialuminides is negative while it is positive for most other aluminides [40].

A negative Cauchy pressure indicates that the angular character to the atomic bonding is

important. In other words, materials with negative values of Cauchy pressure have highly

directional bonding, instead of homogeneous metallic bonding. The directional bonding increases

the bond energy resulting in a high melting temperature for Ir (2410°C) and a high ordering

energy for NisAl. It also necessitates the formation of grain boundary cavities in high angle

boundaries because the directionality of the bonding across such a boundary can only be maintained by decreasing the local packing efficiency. Therefore Ir would have an intergranular

cracking-resistance similar to that of N&Al, as indicated by our results.

Conclusions

In B-free Ni3Al and pure Ir:

1. Low angle (Cl) boundaries and symmetrical C3 boundaries (twins) are particularly strong.

2. Other possible strong boundaries are not sufficiently numerous to be identified. 3. All other high boundaries have similarly low strength, independent of their c values.

4. In particular, low c, high angle boundaries, as a group, are not strong.

5. These results qualitatively agree with predictions based on the structural unit model. 6. This means that 1) Ni3Al and Ir have similar boundary structure and 2) the fracture strength of

an intergranularly brittle polycrystalline aggregate can be increased only by increasing the fraction of low angle and symmetrical C3 boundaries.

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